Problem: Simplify the expression. $(-5z^{4}+z^{3}-2z^{2})(-3z^{4}+6z^{3})$
Solution: First use the distributive property. $ - 5 z^4 (-3 z^4) - 5 z^4 (6 z^3) + z^3 (-3 z^4) + z^3 (6 z^3) - 2 z^2 (-3 z^4) - 2 z^2 (6 z^3) $ Simplify. $ 15z^{8} - 30z^{7} - 3z^{7} + 6z^{6} + 6z^{6} - 12z^{5} $ $15z^{8}-33z^{7}+12z^{6}-12z^{5}$ Identify like terms. $ { 15z^{8}} \color{#DF0030} {- 30z^{7}} \color{#DF0030} {- 3z^{7}} {+ 6z^{6}} {+ 6z^{6}} {- 12z^{5}} $ Add the coefficients. $ { 15z^{8}} \color{#DF0030} { -33z^{7}} {+ 12z^{6}} { -12z^{5}} $